London's FTSE-100 index of leading shares rose slightly on Tuesday, gaining 4.57 points to end the day on 5889.22, a 0.1% rise.
"Overall, there hasn't been too much excitement in the markets today," said CMC Markets analyst David Madden.
"Restrictions in some countries, because of the health crisis, are tighter and with the way things are going in terms of the number of new coronavirus cases, there are fears that further restrictions could be in the offing."
London's top index was helped higher by British Airways owner IAG, which saw a growth spurt, rare in Covid-19 times, after news that passengers flying to Hong Kong and Italy can get one-hour virus tests at Heathrow Airport.
These destinations require passengers to test themselves before departing the country of travel.
IAG's shares jumped by 6.9%.
France's CAC 40 index was flat and the Dax in Frankfurt dropped by 0.9%.
Across the Atlantic the S&P 500 and Dow Jones were both up by around 0.5% by the time markets closed in Europe.
However, Spreadex analyst Connor Campbell said that US politics could affect markets in New York later in the day.
"More volatility could still be expected in the run-up to Nancy Pelosi's stimulus deadline this evening," he said.
"That is unless investors are now comfortable with the assumption a deal isn't getting done this side of the election, based on Joe Biden's consistent lead in the polls (and the sizeable relief package a blue wave would likely produce)."
In company news, shares in housebuilder Bellway dropped by 3.7% after its profits dropped by nearly two-thirds and it revealed a £46.8 million charge after the Grenfell fire forced it to change cladding on some of its buildings.
Reckitt Benckiser closed up 0.01% after revealing that sales in the three months to the end of September rose by 6.9%.
Britvic, which makes Robinsons fruit drinks, said that it will accelerate its shift to 100% recycled plastic for its drinks bottles.
Shares were up 6.4%, but that was likely more to do with the 20-year deal it signed to produce and sell drinks from PepsiCo.
A barrel of Brent crude oil was 0.4% cheaper at $42.45 by the end of play in Europe.
The biggest risers on the FTSE-100 were IAG, up 6.85p to 106.85p, Informa, up 19.3p to 436.9p, Melrose Industries, up 4.85p to 134.45p, Intercontinental Hotel Group, up 150p to 4330p, and Rolls-Royce, up 7p to 227p.
The biggest fallers on the FTSE-100 were Hargreaves Lansdown, down 28.5p to 1380.5p, Taylor Wimpey, down 2.15p to 115.15p, Avast, down 9.5p to 513p, Bunzl, down 44p to 2500p, and Just Eat Takeaway, down 168p to 9750p.
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